No.1765 (NSR)

FCCP contains the definition for “Help Free Play” (which was a direct translation of the French “Aide Libre”):
Help Free Play
A series of moves, of a length equal to the indicated number of moves, some played by White, some by Black, is made in order that after the last move, the aim is reached by White.

While extending the concept to HS# and Direct#, I have used the term “Mixed”.
What Joost and Georgy have stated is mostly equivalent.
In a mixed stipulation of N moves, the Nth move will always be by a particular side. The remaining N-1 moves can be played as any combination of White and Black moves or series. Any check being the last move of a series.
Series movers have also been defined as one side “passing”, so Georgy’s definition is valid.
Joost’s definition is related to combinatorics. The total number of combinations being 2^(N-1). Some of these combinations can be duplicated, like BWW and BBW here. And in some problems, some combinations may not be present, unlike here.
Another related mathematical concept is the Partition of integers: the different ways of writing an integer as the sum of non-negative integers. For N = 2, the combinations are 2 and 1+1. Adding colours gives 2(W), 2(B), 1(W)+1(B) and 1(B)+1(W).
Kabe Moen (a math professor!) commented: “…there might be intriguing mathematical/combinatorial aspects to explore in the general form.“, in his post(5) on the MatPlus forum about this type of stipulation.